Calculating the Diameter of a Tungsten Filament
What is the resistance of a 2.5 cm length of tungsten filament in a small lightbulb?
The resistance of a 2.5 cm length of tungsten filament in a small lightbulb is 0.045 .
Calculating the Diameter of a Tungsten Filament
To calculate the diameter of a 2.5 cm length of tungsten filament in a small lightbulb if its resistance is 0.045 , we need to use the formula for resistance of a wire: R = ρL/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.
First, we need to determine the resistivity of tungsten. The resistivity of tungsten at room temperature is 5.6 x 10^-8 Ωm. Next, we need to rearrange the formula to solve for A: A = ρL/R. Plugging in the given values, we get: A = (5.6 x 10^-8 Ωm) x (2.5 cm) / 0.045 Ω A = 3.11 x 10^-6 m^2 Now, we can use the formula for the area of a circle to find the diameter: A = πr^2, where π is pi and r is the radius (half the diameter). Rearranging the formula, we get: r = √(A/π) r = √(3.11 x 10^-6 m^2 / 3.14) r = 3.15 x 10^-3 m Finally, we can find the diameter by doubling the radius: d = 2r d = 2 x 3.15 x 10^-3 m d = 6.30 x 10^-3 m or 6.30 mm (rounded to two significant figures) Therefore, approximately 6.30 mm is the diameter of the tungsten filament in the small lightbulb.